Extending the dynamic range of biomedical micro-computed tomography for application to geomaterials

Abstract

BACKGROUND:

X-ray computed tomography (CT) can non-destructively examine objects by producing three-dimensional images of their internal structure. Although the availability of biomedical micro-CT offers the increased access to scanners, CT images of dense objects are susceptible to artifacts particularly due to beam hardening.

OBJECTIVE:

This study proposes and evaluates a simple semi-empirical correction method for beam hardening and scatter that can be applied to biomedical scanners.

METHODS:

Novel calibration phantoms of varying diameters were designed and built from aluminum and poly[methyl-methacrylate]. They were imaged using two biomedical micro-CT scanners. Absorbance measurements made through different phantom sections were fit to polynomial and inversely exponential functions and used to determine linearization parameters. Corrections based on the linearization equations were applied to the projection data before reconstruction.

RESULTS:

Correction for beam hardening was achieved when applying both scanners with the correction methods to all test objects. Among them, applying polynomial correction method based on the aluminum phantom provided the best improvement. Correction of sample data demonstrated a high agreement of percent-volume composition of dense metallic inclusions between using the Bassikounou meteorite from the micro-CT images (13.7%) and previously published results using the petrographic thin sections (14.6% 8% metal and 6.6% troilite).

CONCLUSIONS:

Semi-empirical linearization of X-ray projection data with custom calibration phantoms allows accurate measurements to be obtained on the radiodense samples after applying the proposed correction method on biomedical micro-CT images.

Keywords

Micro-computed tomography beam hardening geomaterials empirical correction astromaterials meteorites

1 Introduction

With recent hardware advances in micro-computed tomography (micro-CT), non-destructive CT analysis can be implemented on previously incompatible geomaterials such as meteorites, core samples, minerals, and soil samples. Acquisition of micro-CT images of geomaterials enables rapid compositional analysis and provides archival advantages over destructive methods. However, micro-CT can suffer from dynamic range-limiting artifacts that can obscure detail and limit quantitative and qualitative analysis. Micro-CT imaging provides overall resolution comparable to traditional destructive qualitative analysis methods (i.e. thin-sectioning, which traditionally has low out-of-plane sampling resolution) and also enables additional qualitative and quantitative analysis. The non-destructive nature of micro-CT is especially advantageous for use with specimens that cannot be sectioned [1]. Examples of such specimens that are of particular interest to the geoscientist include: rare samples in both private and museum collections, samples where destruction would inhibit future research (soil peculation, pycnometry), or for initial scout work [2], where micro-CT can be used to determine the best locations for sectioning [3], where 3D information is required for analysis [4], or a litany of other uses [5]. There is also an increased interest in using biomedical scanners in the geological field for those who have easier access to these scanners than less available specimen scanners [2, 6].

While high-energy industrial non-destructive testing CT scanners can be used, micro-CT scanners built for biomedical applications are ideal for use in geomaterial analysis because they: 1) are more commonly available, 2) are installed at an increasing number of university research centers; 3) have higher spatial resolution, appropriate for small specimens; and 4) allow the specimen to remain stationary (in comparison to industrial scanners, which typically rotate the specimen, potentially disrupting samples). Unfortunately, most biomedical micro-CT scanners do not have an adequate dynamic range to study dense objects and often are only available with a lower peak voltage (90 – 120 kVp) when compared with industrial units (>200 kVp).

Although x-ray photons at the lower energies can penetrate most geomaterial samples, artifacts are common when imaging dense materials. These artifacts arise due to three sources of error: 1) beam hardening – an artifact due to the preferential removal of low-energy photons in a poly-energetic spectrum, 2) photon scatter, and 3) under-ranging – the low dynamic range condition that occurs when very few photons are detected (dark signal) making differentiation of different densities and thicknesses difficult. Typical artifacts resulting from these sources of error are incorrectly reconstructed values in the interior of specimens, which confounds quantitative analysis, and streak artifacts from the denser objects that obscure details both on the interior and exterior of specimens. As previously mentioned, similar corrections have been proposed in the past [2, 7–2]. However, these studies either obtain data from a heterogeneous phantom or fail to provide adequate mathematical results of their findings. Additionally, none of these studies examined how their corrections would affect materials of other densities in a non-homogeneous sample.

We present a simple correction for x-ray beam hardening and scatter that can be readily applied to available biomedical scanners. The correction takes the form of a semi-empirical calibration method that can be applied to the raw x-ray absorbance data, prior to CT reconstruction. The correction relies on the acquisition of calibration data using materials of known composition and thickness using the x-ray protocols to be used for specimen scanning. Numerical fits to the empirical calibration data are generated to produce a correction function that is able to linearize the absorbance projection data, thereby removing (or at least reducing) the cupping artifacts and streaks caused by beam hardening and scatter. The proposed correction method is described, implemented, and tested on two different biomedical micro-CT scanners. Two numerical functions are explored for two separate calibration materials and evaluated for their ability to reduce the aforementioned artifacts. Finally, an example correction of a micro-CT scan of a meteorite is also presented. This improves on the existing methodology by providing a simple calibration method that can be obtained from a single projection, including mathematical results to the correction on both the calibration material, as well as a secondary material to account for non-homogeneous materials. We show with a real world example that with proper correction it is possible to produce usable images of dense geo-material from a non-filtered laboratory biomedical scanner.

2 Methods

2.1 Theoretical basis of the correction method

The Beer-Lambert law, which relates the absorbance of photons and a material’s attenuation properties, states: $I = I_{0} e^{- μ x},$ where I is the measured intensity at the detector, I _o is the incident intensity, μ is the energy-dependent linear attenuation coefficient of the material, and x is the path length traveled by the x rays though the material. Based on this relationship, the absorbance A can be easily calculated as: $A = ln (I_{0} / I) = μ x .$ (1)

From Equation 1, the relationship between absorbance and material thickness is linear for mono-energetic x-ray beams, in the absence of scatter. Deviations from this relationship arise with poly-energetic x-ray beams (as are typically used in micro-CT scanners). When poly-energetic beams are used, the low-energy photons are absorbed preferentially, resulting in a “harder beam” (i.e. the mean energy of the transmitted x-ray spectrum is higher than that of the incident x-ray spectrum). As a result, relatively more photons will pass through the sample than if a mono-energetic x-ray beam (of an effective mean energy and effective flux) was used. In addition, scattering of x-rays within the material also results in an increase of detected photons. By “mimicking” decreased absorbance, both beam hardening and scatter result in an underestimation of the material’s attenuation coefficient, particularly for longer path lengths through the material. The artifacts following the CT reconstruction process, appear as “cupping” in the CT image (i.e. decrease of measured attenuation coefficient in the center of the image, compared to the edges of the object). Figure 1 is a representative plot of the measured absorbance as a function of material thickness, demonstrating the expected non-linear relationship.

The artifacts resulting from beam hardening and scatter can be reduced by implementing a correction that is based on a curve fit of empirically acquired absorbance data of objects with known materials and thicknesses. Previous authors have used point-to-point linear [10] and polynomial [8] fits to the empirically derived absorbance data; Herman’s original beam hardening correction showed negligible improvement in artifact reduction when increasing the polynomial order above two (i.e. A = ax ² + bx, where a and b are constants). For this study, and based on the non-linear shape observed in Fig. 1, we also considered a functional form that increases monotonically to a plateau value, i.e. inverse exponential decay as described below:

Fig.1

Idealized plot of absorbance vs. material thickness to demonstrate the effect of beam hardening and scatter. The straight line represents the response expected from Equation 1. This non-linear curve (dashed line) represents the measured absorbance.

$A = P (1 - e^{(Kx)}) .$ (2) where in Equation 2, P is the absorbance at infinite thickness (the plateau) and K is a rate constant.

The fitted functions can then be used to linearize the data by rearranging the formulae to solve for the thickness from the recorded absorbance. This effectively remaps the observed absorbance data to linearized (i.e. corrected) values on a pixel-by-pixel basis, for each projection view. The linearization of a second-order polynomial results in the equation: $x = \frac{- b + \sqrt{b^{2} + 4 aA}}{2 a}$ (3) while the linearization of the inverse exponential decay results in the equation: $x = ln \frac{(P - A)}{P} / - K .$ (4)

2.2 Calibration phantom

For the empirical determination of absorbance vs. material thickness curves, two calibration phantoms (i.e. calibration objects) were designed and built. Each phantom was fabricated of a single material and covered a range of thicknesses appropriate for the range of anticipated applications. The phantoms comprised eight coaxial cylindrical plates with known diameters ranging from 4.5 mm to 60 mm arranged in in an alternating pattern to mimic the general shape of geomaterial specimens, as shown in Fig. 2. One calibration phantom (Fig. 2a) was manufactured using poly[methylmethacrylate] (PMMA, Lucite), which mimics soft, water-like materials typically used in biomedical applications [10]; the PMMA plate thickness was 4.8 mm. The second calibration phantom (Fig. 2b) was manufactured using aluminum (6061-T6) to mimic dense objects like bone, silicate minerals, and other geomaterials with similar electron densities; the Al plate thickness was 6.4 mm. To ensure larger areas of uniform thickness on each plate, two opposing sides were flattened prior to imaging. Using these calibration phantoms, a single x-ray projection image yields the eight absorbance measurements (Fig. 2c, d) required to determine characterize the relationship between absorbance and material thickness.

Fig.2

Calibration phantoms for beam hardening correction in CT. Phantoms were fabricated from a) PMMA and b) aluminum. Note the flattened areas on each plate, machined to provide a larger measurement area. The scale cube (1 cm) provides a size reference. Representative absorbance images of the PMMA (c) and aluminum (d) phantoms are also shown.

2.3 Micro-CT scanners

Two biomedical laboratory micro-CT scanners were used in this study to validate the versatility of the methods. Both scanners utilize cone-beam geometry, where the x-ray source and detector rotate around the specimen.

The GE eXplore Ultra (GE Healthcare, London Canada) is a large-bore (20 cm) slip-ring gantry scanner designed for rapid and fast throughput imaging. The operation and characterization of the scanner have been described in detail previously [11]. Briefly, 1000 projection views, of matrix size 1024×680, are obtained over a single 16-second scan covering 360°. Corrections for bad detector elements, pixel-to-pixel non-uniformity, and dark current were performed prior to cone-beam CT reconstruction. The resulting three-dimensional (3D) images have a transaxial field of view of 14 cm and axial extent of 10.4 cm and an isotropic voxel spacing of 154μm [11]. For all experiments in this study the x-ray beam parameters used on the Ultra scanner were 120 kVp and 20 mA.

The second scanner was a GE eXplore speCZT (GE Healthcare, London Canada) scanner, which is a step-and-shoot device with an 89 mm bore size. For each scan, 900 views were obtained in 0.4° increments, with an exposure interval of 16 ms per frame; the total scan time was 5 minutes. The reconstructed CT images have a transaxial field of view of 70 mm and cover an axial extent of 5.4 cm; the voxel spacing on this scanner, with this acquisition protocol, is 50μm, isotropic. For all experiments in this study the x-ray beam parameters used on the speCZT scanner were 90 kVp and current of 40 mA. All data was reconstructed into signed 16-bit data; this extends the dynamic range of the CT data in Hounsfield units to a maximum of 32,767 HU.

2.4 Acquisition and analysis of calibration data

For each scanner, calibration was performed using both the aluminum and PMMA phantoms. Each phantom was placed on the scanner bed and the source-detector system was oriented perpendicular to the flat edges of the calibration phantom. A single x-ray image of each phantom was acquired and was sufficient to generate measurements of absorbance for all thicknesses. The images were corrected for detector-element non-uniformity, then converted to absorbance images (Fig. 2c, d) prior to analysis. ImageJ software (National Institutes of Health, Bethesda, MD) was utilized for analyzing the absorbance images. Regions of interest (ROI) – 4×4 pixels – were placed on each of the flat regions of each plate (representing a different thickness) of each phantom and the mean and standard deviation of the absorbance were recorded.

The absorbance-thickness relationships were fitted using non-linear Levenberg-Marquardt fitting in Prism (GraphPad Software, Inc., La Jolla, CA). As described above, both a second-order polynomial [8, 12] and the one-phase exponential decay function (Equation 2) were fitted. Calibration fits were obtained using both fitting functions for each scanner and both the aluminum and PMMA phantoms.

2.5 Implementation of beam hardening correction

To incorporate the beam hardening (and scatter) correction prior to reconstruction, custom software was written to linearize each absorbance value on a pixel-by-pixel basis for each projection image acquired. Linearization was performed using Equations 3 and 4 for the polynomial and inverse exponential decay fitted functions. It is important to note that the linearization process results in values of absorbance that are floating point numbers ranging up to approximately 5, for geomaterials. While some reconstruction software can accept the floating-point absorbances (e.g., the reconstruction software used with the Ultra scanner data) others (e.g. the speCZT scanner) requires absorbance data be saved as 16-bit integer values. In the latter, the linearized absorbances must be rescaled prior to reconstruction, while taking care that the scaled values do not exceed the maximum 16-bit integer range.

2.6 Evaluation of beam hardening correction using single-material test objects

2.6.1 Image acquisition, correction, and reconstruction

To evaluate the effectiveness of the beam hardening correction micro-CT scans were acquired of PMMA and aluminum rods with diameters ranging between 12.7 and 63.5 mm. Rods of a single material were chosen as objects to evaluate the correction technique, because they provided an easy way to check the uniformity of the corrected images and because the shape approximates the shapes of most geomaterial specimens. For the PMMA rods, reconstruction was performed with no beam hardening correction and following correction using each of the four correction “methods”: poly-Al and poly-PMMA, polynomial fits using Aluminum or PMMA calibration data, respectively and exp-Al and exp-PMMA, inverse exponential decay fits using Aluminum or PMMA calibration data, respectively. For the aluminum rods, the same approach was used but correction using the PMMA calibration data was not performed, as it was not expected to yield successful results on a material with significantly higher attenuation. Correcting the PMMA rod data with the Al-calibration results allowed us to investigate the possibility to correct materials of lower attenuation using calibration data obtained with more highly-attenuating materials, which in practice would facilitate the incorporation of a single correction method on each scanner for use with both biomedical specimens and geomaterials.

Following reconstruction, images were scaled in Hounsfield Units (HU) – the unit typically used in clinical CT scans. The HU scale is a linear scale where air is defined as – 1000 HU and water as 0 HU; in these units geomaterials have values that range above 2000 HU and metals are higher, with values above 4000 HU.

2.6.2 Analysis of reconstructed images (cupping)

Reconstructed images were analyzed using ImageJ. For each test-rod image, nine 4×4 voxel ROIs were drawn – one at the center, four at the edges of the rod, and four in the air surrounding the rods, as shown in Fig. 3. From these measurements, the extent of cupping was calculated as follows: $cupping = 1 - \frac{(C - B)}{E - B}$ (5)

Fig.3

Locations of the nine regions of interest used to calculate percent cupping for the test rods. The image shown in this image is from the 63.5 mm PMMA cylinder scanned on the speCZT scanner.

In Equation 5, E, C and B are the average voxel values in the edge, center and background air, respectively. Averages and standard deviations of cupping (percent) were calculated for five slices of each reconstructed image of a PMMA or Al test rod. Additionally, lines were drawn through the center of each image and the image intensities were plotted to enable visual evaluation of the effectiveness of the corrections.

2.7 Example application of beam hardening correction using a geomaterial

The ultimate application of the proposed semi-empirical correction technique is to improve the uniformity and accuracy of scans of geomaterials, such as meteorites. As a proof-of-principle example, we have applied the derived calibration curves to correct a representative geomaterial sample, in this case a 2.5 cm³ sample of the fresh Bassikounou meteorite (H5 chondrite), which fell on Oct 16, 2006 [13]. The specimen was scanned using the speCZT scanner, with the same acquisition parameters as all other test objects (90 kVp and 40 mA). Absorbance data were corrected using the poly-Al calibration and 3D images were reconstructed using both corrected and un-corrected. Line profiles were drawn through the reconstructed images to demonstrate the reduction in cupping artifact. Furthermore, volumetric analysis was performed to quantify the metallic fraction (by volume) of the meteorite.

3 Results

3.1 Calibration

Both non-linear fit functions fit the experimental data acquired from both scanners and both calibration phantoms with an R² >0.99; details are provided in Fig. 4 and Table 1. As expected, both scanners yielded similar results, but different fit parameter values. The differences are attributed to the fact that the images were acquired with different x-ray energies and using different detectors. In addition, the scanners store absorbance values in different data formats and scale the data differently.

Fig.4

Plots of absorbance vs. thickness for the aluminum and PMMA calibration phantoms scanned in the Ultra (a) and specCZT (b) scanners. The symbols represent the measured data (error bars are plotted, but in most cases are smaller than the symbol size). The lines represent the polynomial (poly) and inverse exponential (exp) fits as indicated in the legend.

Table 1

Fitting parameters for each of the beam-hardening correction methods. The parameters apply to acquisitions with 120kVp, 20 mA×rays (Ultra) and 90 kVp, 40 mA×rays (speCZT)

		Ultra Scanner			speCZT Scanner
Material	Fit	a (or P*)	b (or K*)	R²	a (or P*)	b (or K*)	R²
PMMA	polynomial	– 2.431×10^–5	0.0238	0.9999	– 9.079×10^–2	51.49	0.9999
	inv. exp. decay*	– 10.97	2.173×10^–3	0.9999	– 13235	3.904×10^–3	0.9999
Al	polynomial	– 5.034×10^–4	0.0864	0.9999	– 1.858	227	0.9977
	inv. exp. decay*	– 5.281	0.01723	0.9996	– 8445	0.03102	0.9995

3.2 Evaluation using PMMA and Al test rods

3.2.1 PMMA test rods

Sample images from the uncorrected and corrected images of the largest the PMMA test rod (63.5 mm diameter) are shown in Fig. 5 for both scanners; percent cupping is plotted for all tested rod diameters and correction methods in Fig. 6. As expected, the effect of beam hardening and scatter can be seen as slight cupping in the uncorrected images (Fig. 5) and increases with rod diameter (Fig. 6). The differences between acquisition protocols cause variations in the amount of cupping seen in the individual samples. Corrections using the PMMA calibration phantom (poly-PMMA and exp-PMMA) do not only reduce or slightly modify the cupping artifact, but also perform nearly identically for both scanners. Correction using the aluminum calibration phantom (poly-Al and exp-Al) perform differently on the two scanners. On the Ultra scanner, aluminum calibrated corrections perform worse than the PMMA calibrated corrections, causing values in the center to be higher than the edges of the sample (herein referred to as overcorrection). However, on the speCZT the aluminum calibrated corrections outperform those calibrated with PMMA, with the poly-Al correction performing better than the exp-Al correction, and similarly to the PMMA corrections, keeping the central values within 5% of the values at the edges.

Fig.5

Cross-sectional images of the 63.5 mm diameter PMMA rod scanned on Ultra (a) and speCZT (b) scanners. The plots are signal intensity profiles through the line drawn in each image. The first column shows uncorrected data, followed by images corrected using the poly-PMMA, exp-PMMA, poly-Al, and exp-Al methods, as indicated in the figure. Note, the differences in noise characteristics between the two scanners (evident in the line profiles) are due to the differences in acquisition protocol and voxel sizes.

Fig.6

Percent cupping calculated for the PMMA test rods plotted as a function of rod diameter for the Ultra (a) and speCZT (b) scanners for each of the correction methods. The values plotted are means and standard deviation from 5 adjacent image slices.

3.2.2 Aluminum test rods

Figure 7 shows uncorrected and corrected images of aluminum test rods scanned on the Ultra (Fig. 7a) and speCZT (Fig. 7b) scanners. As expected, the cupping artifacts in the uncorrected aluminum rods are significantly greater than those observed in the PMMA rods. Quantitative values of percent cupping are plotted in Fig. 8 for the two scanners, demonstrating the expected increase in artifact with increasing rod diameter. Following correction using both polynomial and inverse exponential functions, the percent cupping is significantly reduced for all test rods scanned on the Ultra scanner and for all but the largest (50.8 mm diameter) rod scanned on the speCZT. The polynomial fit (poly-Al) outperformed exp-Al across the range of test rod diameters, resulting in smaller percent cupping. On the Ultra scanner (Fig. 8a) both correction methods had a tendency to overcorrect the samples (i.e. – ve percent cupping); this tendency also occurred within exp-Al corrections of the speCZT tests (Fig. 8b). On the speCZT scanner, the 50.8 mm test rod caused extreme cupping, exceeding 30%. When correction was attempted, with either method, very high noise values and over correction occurred, making correction impossible in this case.

Fig.7

Cross-sectional images of aluminum test rods rod scanned on Ultra (a) and speCZT (b) scanners. The plots are signal intensity profiles through the line drawn in each image. The first column shows uncorrected data, followed by images corrected using the poly-PMMA, exp-PMMA, poly-Al, and exp-Al methods, as indicated in the figure. The rod shown for the ultra is the 50.8 mm diameter one, while the diameter of the rod in (a) (speCZT) is 38.1 mm. Note, the differences in noise characteristics between the two scanners (evident in the line profiles) are due to the differences in acquisition protocol and voxel sizes.

Fig.8

Percent cupping calculated for the aluminum test rods plotted as a function of rod diameter for the Ultra (a) and speCZT (b) scanners for the two correction methods based on the aluminum calibration phantom. The values plotted are means and standard deviation from 5 adjacent image slices.

3.2.3 Application to meteorite specimen analysis

Example cross-sectional images from the Bassikounou (H5 chondrite) meteorite sample are shown in Fig. 9. There are two distinguishable phases in the sample – a high radiodense metallic phase (consisting of kamacite and taenite), which is surrounded by bulk material. It can easily be seen from the uncorrected images (Fig. 9a), that the centre of the meteorite is darker than the surroundings; this cupping is also clearly seen in the profile of signal intensities (Fig. 9c, yellow). Following correction using the exp-Al method, the cupping is removed and the background material has uniform intensity throughout the image (Fig. 9b, and red profile in c). Calculations of the meteorite volume (counting all voxels with intensities above a threshold of 2000 HU) and the volume of metallic (radiodense) inclusions (threshold of 9650 HU) are presented in Table 2 for the uncorrected and corrected images.

Fig.9

Beam hardening correction of the Bassikounou meteorite sample. Uncorrected (a) and corrected (b) cross-sectional images were collected at 110 kVp and 40 mA and reconstructed at 50μm/voxel. The bright inclusions in both images represent denser materials – most likely kamacite and taenite. The profile plots in (c) clearly demonstrate the improvement in uniformity across the specimen, which enables the “extraction” of metallic inclusions using a single threshold value. The dotted line in (c) is intended as a guide to evaluate lack of cupping visually.

4 Discussion

4.1 Calibration phantoms

In this study we have shown that biomedical micro-CT scanners can be used to analyze geomaterial specimens following correction for beam hardening and scatter. The correction step requires multiple thicknesses of a material, with x-ray absorption properties similar to those of the samples to be scanned, to be imaged with a fixed protocol. While an estimate of the change in absorbance with thickness can be obtained by sequentially imaging samples of different thicknesses, the phantoms presented in this study enable calibration to be performed in a single step. Furthermore, the shape of the phantoms – involving plates of varying diameter arranged in an alternating manner on either side of the largest plate – mimics not only the beam hardening effect, but also mimics the effect of scattered photons. It is important to note that the calibrators provide estimates of the two effects and cannot mimic either perfectly for a range of applications.

In this study we used an aluminum calibration phantom to estimate the parameters for the beam-hardening correction methods. We expect that for tailored applications, phantoms can be made of different materials – e.g. a concrete phantom of similar shape to those shown in Fig. 2 could be used to calibrate for scans of concrete cylinders; phantoms could also be molded of clay or machined out of granite for further examination of those materials.

4.2 Correction for cupping artifacts

The results in Fig. 5 through 8 clearly demonstrate that the proposed correction methods effectively reduce the cupping artifacts. Linearization of the projection data prior to reconstruction effectively extends the dynamic range, enabling the reconstruction of denser and thicker objects. In the present study, effective correction was achieved on both scanners for both PMMA and aluminum test rods. Overall, the correction using the aluminum calibration phantom and the second order polynomial fit to the calibration data (poly-Al) yielded the best results overall, with |percent cupping|<5.9% for all PMMA test rods and <4.1% for all aluminum rods in diameter smaller than 38 mm.

For the large diameter (50.8 mm) Al-test rod the Ultra scan, corrected with poly-Al yielded good correction (|percent cupping|=8.5%), however the scan of the same rod on the speCZT scanner could not be corrected effectively (|percent cupping|=45%), which was in fact worse than the uncorrected result. This result is attributed to the fact that a higher-energy spectrum was (120 kVp) was used on the Ultra scanner, compared to the 90 kVp used on the speCZT scanner. At the lower energy, very few x-ray photons penetrate the full thickness of the Al rod, resulting in “under ranging” – the signal (I) at the detector is nearly zero and it is impossible to differentiate between different thicknesses based on I. In this case the correction step only amplifies the noise in the image and results in even worse non-uniformity across the sample. Therefore, it is important to select a scanning protocol with the highest possible x-ray energy spectrum and highest current and to check for the sufficient photon flux though the highest attenuating path prior to applying correction. (Note, the speCZT scanner is capable of generating x-ray spectra with energies as high as 110 kVp. However, for this study we chose to use 90 kVp in order to demonstrate the ability to correct dense materials, including geomaterials, even at this low energy.)

Table 2
Volumetric analysis of Bassikounou meteorite sample

Uncorrected Corrected

Volume (mm³) Volume Fraction (%) Volume (mm³) Volume Fraction (%)

background 5.87 96.9 5.20 86.3

dense materials 0.19 3.1 0.82 13.7

total 6.06 100 6.02 100

	Uncorrected	Corrected
background	5.87	96.9	5.20	86.3
dense materials	0.19	3.1	0.82	13.7
total	6.06	100	6.02	100

Although we have found the aluminum calibrated polynomial fitted beam-hardening correction to be the most effective method in the present study, it may be important to evaluate different fitting functions for different scanners and protocols. In addition, even for the scanners used in this study the calibration step must be repeated for each protocol (various kVp) that is to be used.

Furthermore, it is important to note that the presented correction method can be applied retrospectively to existing data – provided the projection images are available – offering the ability to re-evaluate previously scanned specimens.

4.3 Use of biomedical micro-CT scanners for imaging geomaterials

A goal of this study was to determine scanning and beam hardening correction protocols that will allow micro-CT scanners designed for biological applications (e.g. imaging of experimental rodents) to be applied to geomaterials for non-destructive testing. In general, biomedical micro-CT scanners are less expensive, compared to specialized industrial CT scanners, and are ubiquitous at academic institutions. By demonstrating that the same beam-hardening correction method (poly-Al) can be used to correct both dense objects (aluminum rods) and objects mimicking soft biological tissues (PMMA rods) the scanners can implement a single correction for both biomedical and geological applications.

In addition, biomedical scanners also offer the advantage that a majority employ rotating source-detector geometry, allowing the sample to remain stationary during the scanning process. By minimizing the disruption of sensitive samples, the use of biomedical scanners for geophysical samples may extend the use of CT to an increasing number of applications, such as pore and flow analysis of soils.

4.4 The presented correction in the context of prior beam-hardening correction algorithms

Semi-empirical corrections for beam hardening have been described and adopted in the past, including the approach originally described in 1976 [14] and later expanded by Herman [8], who demonstrated excellent correction using a quadratic polynomial fit. Despite the introduction of correction algorithms almost as soon as CT was invented, work in this area continues to this day – even in the medical field. Beam hardening can be reduced at the cost of photon flux by using the filtration and has been shown to reduce cupping in water phantoms [15]. A post-reconstruction method using re-projections of CT objects and corrections using curves based on aluminum has been shown to reduce beam hardening in aluminum up to 14% [10]. While these methods can also be applied to geomaterials, they employ intermediate stage corrections performed on the original or re-projected CT data, and often require knowledge of the CT reconstruction process to apply the correction. The simple correction methods presented here can – in general – be applied to the projection data off line, then returned to the scanner for CT reconstruction.

4.5 Application to a meteorite sample

Corrected images of the scanned Bassikounou (H5 chondrite) meteorite sample (Fig. 9) clearly demonstrate that the beam-hardening artifact (cupping) was minimized following correction. If a single threshold value is selected as a cut-off for differentiating metallic inclusions from background material the majority of the inclusions in the centre of the sample are not counted (see profiles in Fig. 9c). In fact, even the brightest (densest) inclusion seen in the middle of the selected profile is barely included in the cumulative volume count in the uncorrected images; however, it is clearly above the threshold when the image is corrected. Earlier destructive studies, using thin sections, studying the composition of another sample from the same meteorite have reported metallic content at 8% by volume, with an additional 6.6% by volume of polycrystalline troilite [13] – both of which would appear as radiodense inclusions in the CT scans. The agreement between this prior report (14.6% by volume as the sum of metal plus troilite) and the results from the corrected micro-CT image (Fig. 9b, Table 2) of 13.7% by volume is excellent and suggests that beam-hardening corrected micro-CT using a biomedical scanner can be used for non-destructive analysis of meteorite samples. These encouraging results also suggest that additional micro-CT analysis – e.g. using dual energy approaches [16, 17] – could be used for even more detailed composition analysis. The methodology presented here has been used to correct reconstructions of a range of materials, from spinal tissue [18] to meteoritic samples [19, 20]. The restoration of grayscale values more representative of the material’s given x-ray properties enables effective quantitative analysis that is normally not feasible in CT data of radiodense materials scanned with low-energy polychromatic x-ray sources.

5 Conclusion

A simple beam-hardening correction method – applied to the x-ray absorbance data prior to CT reconstruction can be used to effectively reduce beam-hardening artifacts when using a biomedical scanner to evaluate geomaterials. The novel calibration step phantom, constructed of a material that mimics the attenuation properties of the materials to be scanned (e.g. aluminum), can be used to acquire the required absorbance calibration data from a single image acquisition. While various numerical functions can be fit to the data, the present study demonstrates that – for the scanners evaluated – correction using a second order polynomial fit yields the best reduction in cupping artifacts (better than 5%) for objects as wide as 40 mm in diameter. Biomedical micro-CT scanners can easily be adapted to provide high-quality, artifact free images of geomaterials for quantitative non-destructive analysis.

Footnotes

Acknowledgments

Funding for this project was provided by the Natural Sciences and Engineering Research Council of Canada, grant numbers 386395, 4294, and RGPIN-2016-06048. DWH is the Dr. Sandy Kirkley Chair for Musculoskeletal Research at the Schulich School of Medicine & Dentistry. We wish to thank Dr. Phil McCausland, Meteorite Curator at Western University, for the loan of Bassikounou H5 chondrite. We also thank Hristo Nikolov for machining the micro-CT phantoms, and Joseph Umoh for his assistance with the GE eXplore Ultra micro-CT scanning and scan data.

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	Uncorrected		Corrected
Volume (mm³)	Volume Fraction (%)	Volume (mm³)	Volume Fraction (%)
background	5.87	96.9	5.20	86.3
dense materials	0.19	3.1	0.82	13.7
total	6.06	100	6.02	100

Extending the dynamic range of biomedical micro-computed tomography for application to geomaterials

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSIONS:

Keywords

1 Introduction

2 Methods

2.1 Theoretical basis of the correction method

2.4 Acquisition and analysis of calibration data

2.5 Implementation of beam hardening correction

2.6 Evaluation of beam hardening correction using single-material test objects

2.6.1 Image acquisition, correction, and reconstruction

2.6.2 Analysis of reconstructed images (cupping)

3 Results

3.1 Calibration

3.2.1 PMMA test rods

4.1 Calibration phantoms

4.2 Correction for cupping artifacts

Table 2 Volumetric analysis of Bassikounou meteorite sample Uncorrected Corrected Volume (mm3) Volume Fraction (%) Volume (mm3) Volume Fraction (%) background 5.87 96.9 5.20 86.3 dense materials 0.19 3.1 0.82 13.7 total 6.06 100 6.02 100

4.4 The presented correction in the context of prior beam-hardening correction algorithms

4.5 Application to a meteorite sample

5 Conclusion

Footnotes

Acknowledgments

References

Table 2
Volumetric analysis of Bassikounou meteorite sample

Uncorrected Corrected

Volume (mm³) Volume Fraction (%) Volume (mm³) Volume Fraction (%)

background 5.87 96.9 5.20 86.3

dense materials 0.19 3.1 0.82 13.7

total 6.06 100 6.02 100